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We prove that every rationally null-homologous Floer simple knot in a closed, oriented, irreducible three-manifold with nonzero Thurston norm is unknotted. The proof combines a cut-and-reglue comparison for extremal Floer groups with Binns's theorem on Floer-minimal knots in balanced sutured manifolds.
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Zhaojun Chen (2026) studied this question.
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